Mechanical Waves

A tube of air open at only one end is vibrating in the $5^{\mathrm{t}\mathrm{h}}$ harmonic from a tuning fork of frequency 120 $Hz$ placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency tuning fork would be needed at the open end?

(A) 24 Hz
(B) 30 Hz
(C) 40 Hz
(D) 125 Hz
(E) 600 Hz

A new radio station broadcasts its signal with a wavelength of 3.40 $m$. At what frequency is this station broadcasting?

(A) $1.76\times 10^{8}Hz$
(B) $8.82\times 10^{7}Hz$
(C) 100 $Hz$
(D) 0.294 $Hz$
(E) $1.13\times 10^{-8} Hz$

A string, clamped at both ends, has its tension fixed. A wave generator vibrates the string with a frequency $f$ producing waves of wavelength $\lambda$ which have speed $v$. The frequency of the wave generator now is doubled to $2f$. Which one of the following choices best describes the new values of the wavelength of waves produced and the speed of the waves on the string?

Two wave pulses travel to the right toward a rigid boundary as shown. After reflection of the triangular pulse, the pulses will interfere. Which one of the following pictures best represents the superposition of the pulses when the centers of the individual pulses coincide?

(A)

(B)

(C)

(D)

(E)

A standing wave is created in an air-filled tube open at both ends when a tuning fork of frequency 552 $Hz$ is placed near one of the open ends. A tuning fork of frequency 644 $Hz$ produces the next highest harmonic for this tube. What is the length of the open tube? Assume room temperature.

(A) 0.46 $m$
(B) 0.92 $m$
(C) 1.59 $m$
(D) 1.85 $m$
(E) 3.70 $m$

The wave speed is 20.0 $m/s$ for waves traveling on a string tied at both ends. If sinusoidal waves with a frequency of 2.00 Hz are traveling on this string, which one of the following choices best represents the period of these waves?

(A) 40.0 $s$ (B) 10.0 $s$ (C) 3.16 $s$ (D) 0.50 $s$ (E) 0.10 $s$

A 1.50 $m$-long string clamped at both ends is vibrating at its second harmonic. What is the wavelength associated with the string for this scenario?

(A) 3.00 $m$
(B) 2.25 $m$
(C) 1.50 $m$
(D) 1.00 $m$
(E) 0.75 $m$

A tuning fork placed over a 57 cm column of air closed only at its bottom end produces a standing wave in the $3^{\mathrm{r}\mathrm{d}}$ harmonic. The speed of sound in air is $342\displaystyle \frac{m}{s}$. What is the frequency of the tuning fork?

(A) 150 $Hz$
(B) 300 $Hz$
(C) 450 $Hz$
(D) 600 $Hz$
(E) 900 $Hz$

A waterproof speaker placed at the bottom of a swimming pool emits a sound wave that travels toward the surface of the water. In the water, the sound wave has a frequency $f_{waTer}$, wavelength $\lambda_{waTer}$, and wave speed $v_{waTer}$. When the sound wave enters the air it has a frequency $f_{air}$, wavelength $\lambda_{air}$, and wave speed $v_{air}$. Which one of the following relationships correctly compares the frequencies, wavelengths, and wave speeds of the waves in the air and water?

(A) $f_{\text{water}}=f_{\text{air}}$; $\lambda_{\text{water}}=\lambda_{\text{air}}$ ; $v_{\text{water}}=v_{\text{air}}$

(B) $f_{\text{water}}=f_{\text{air}}$; $\lambda_{\text{water}}>\lambda_{\text{air}}$ ; $v_{\text{water}}>v_{\text{air}}$

(C) $f_{\text{water}}<f_{\text{air}}$; $\lambda_{\text{water}}>\lambda_{\text{air}}$ ; $v_{\text{water}}=v_{\text{air}}$

(D) $f_{\text{water}}<f_{\text{air}}$; $\lambda_{\text{water}}=\lambda_{\text{air}}$ ; $v_{\text{water}}<v_{\text{air}}$

(E) $f_{\text{water}}=f_{\text{air}}$; $\lambda_{\text{water}}<\lambda_{\text{air}}$ ; $v_{\text{water}}>v_{\text{air}}$

A standing wave on a string is produced. Which one of the following choices best describes the location on the string at which maximum constructive interference occurs?

(A) node
(B) antinode
(C) harmonic
(D) overtone
(E) amplitude

"Particles of matter also have associated wavelengths and can behave as waves." To which scientist is this concept attributed?

(A) de Broglie
(B) Pauli
(C) Fermi
(D) Heisenberg
(E) Rydberg

A 680 $Hz$ tuning fork is placed over a tube open at both ends that is filled with air. As a result, a standing wave in the $3^{\mathrm{r}\mathrm{d}}$ harmonic is produced. The speed of sound in air is $340\displaystyle \frac{m}{s}$. What is the length of the tube?

(A) 0.38 $m$
(B) 0.67 $m$
(C) 0.75 $m$
(D) 1.33 $m$
(E) 1.50 $m$

Two spherical speakers separated by 30.0 $m$ each emit a constant frequency signal of 57.0 $Hz$ in phase with each other. The speed of sound is $342\displaystyle \frac{m}{s}$. How many locations of complete destructive interference of the incoming signals are there on the line between the speakers?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 6

A radio station broadcasts its signal at a frequency of100.0 $MHz$. What is the wavelength of the station's signal?

(A) 3.00 km
(B) 3.00 $m$
(C) 3.00 mm
(D) 0.33 $m$
(E) 0.33 km

A tuning fork of frequency $f$ is placed over a long tube closed at one end producing the third lowest frequency standing wave for the tube. What frequency tuning fork would be needed to produce the fourth lowest frequency standing wave?

(A)$\displaystyle \frac{4}{3}f \\ (B)\frac{5}{3}f \\ (C)\frac{6}{5}f \\ (D)\frac{7}{5}f \\ (E)\frac{5}{4}f$

A string is connected to a mechanical oscillator on one end and to a cube-shaped mass, $M=8.0kg$, at the other end as shown. The oscillator vibrates the string with a frequency of $f$ producing the standing wave in the figure on the left. When the mass is submerged completely in water, the string vibrates in the standing wave pattern shown on the right.

37. What is the value of the ratio for the tension when the mass is submerged in water to the tension when the mass is hanging in air?

(A) 4
(B) 2
(C)$\frac{1}{\sqrt{2}}$
(D) $\frac{1}{2}$
(E) $\frac{1}{4}$

38. What is the length of one side of the cube of mass $M$?

(A) 0.006 $m$
(B) 0.091 $m$
(C) 0.126 $m$
(D) 0.182 $m$
(E) 0.200 $m$

A traveling sine wave of frequency 3.0 $Hz$ is known to move at 6. $0\displaystyle \frac{m}{s}$ on a string. Which one of the following figures best represents what a one-meter section of the string could look like at an instant of time?

A scientist performs an experiment in which she determines the shortest length of a gas column needed to create resonance for a vibrating tuning fork over a tube closed at one end. She plots the gas column length against the inverse of the frequency for a set of tuning forks and finds that she has a straight line fit through the data. Representing the slope of the line as $m$, which one of the following choices correctly identifies the speed of waves through the gas in the experiment?

(A)$\displaystyle \frac{1}{4}m$
(B) $m$
(C) $2m$
(D) $\displaystyle \frac{4}{3}m$
(E) $4m$

A point wave source travels along the $x$-axis at constant speed $v_{s}$. Stationary observers on the $x$-axis measure the wavelength of the waves that they receive. The ratio of the wavelength measured at a location behind the source to the wavelength measured at a location in front of the source is 1.50. If the wave speed is $v$, what is the source speed $v_{s}$?

(A)$\displaystyle \frac{1}{5}v$
(B)$\frac{1}{4}v$
(C)$\frac{1}{3}v$
(D)$\frac{1}{2}v$
(E)$\frac{2}{3}v$

A 2.0 $\mathrm{m}$ long organ pipe which is open at both ends resonates at its fundamental frequency. Neglecting any end effects, what wavelength is formed by this pipe in this mode of vibration?

(A) 1 meter
(B) 2 meters
(C) 4 meters
(D) 6 meters
(E) 8 meters

A standing transverse wave is formed on a tightly stretched string. The distance between a node and an adjacent antinode is:

(A) 1/8 wavelength

(B) 1/4 wavelength

(C) 1/2 wavelength

(D) 1 wavelength

(E) 0

A student generates a transverse periodic wave on a string. The wave travels away from the student at a constant speed $\mathrm{v}$. Which of the following changes by itself will increase the speed at which the wave travels away from the student?

(A) The student could use the same string but increase the frequency at which they generate the wave.

(B) The student could use the same string but increase the wavelength of the waves they generate.

(C) The student could use the same string but increase the amplitude of the waves they generate.

(D) The student could use a string with the same length and tension, but greater linear density

(E) The student could use the same string, but placed under greater tension.

A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops (antinodes). What frequency is needed if the standing wave pattern is to contain 4 loops (antinodes)?

(A) 12 Hz
(B) 16 Hz
(C) 36 Hz
(D) 48 Hz
(E) 60 Hz

The intensity level is measured to be 60 $\mathrm{d}\mathrm{B}$ at a distance of 15 $\mathrm{m}$ from a speaker. What is the intensity level at a point 2.0 $\mathrm{m}$ from the speaker? Assume that the speaker radiates equally in all directions

(A) 55.7 $\mathrm{d}\mathrm{B}$
(B) 57.5 $\mathrm{d}\mathrm{B}$
(C) 67.0 $\mathrm{d}\mathrm{B}$
(D) 75.5 $\mathrm{d}\mathrm{B}$
(E) 77.5 $\mathrm{d}\mathrm{B}$

The picture shows two speakers, A and B, which emit the same 680-Hz tones in phase. Point P is located 1.000 m directly in front of Speaker A. A sound sensor at Point P records a minimum sound intensity. Speaker B is slowly moved away from Speaker A along the line joining them. How far must Speaker B be moved further from Speaker A until the sound sensor at Point P first records a maximum sound intensity?

(A) 0.368 m
(B) 0.438 m
(C) 0.500 m
(D) 0.686 m
(E) 0.982 m

Consider a traveling wave on a string of length $L$, mass $M$, and tension $T$. A standing wave is set up. Which of the following is true?

(A) The wave velocity depends on $ML, T.$

(B) The wavelength of the wave is proportional to the frequency.

(C) The velocity of a given particle in the string is equal to the wave velocity.

(D) The wavelength is proportional to $T.$

(E) The frequency depends upon $L.$

A person standing 5.0 m from a barking dog measures the sound intensity level to be 65 dB . What would be the intensity level at that same distance if two identical dogs very close to each other are barking?
(A) 34 dB
(B) 65 dB
(C) 68 dB
(D) 130 dB
(E) 136 dB

For ordinary conversation, a sound level meter reads 60 dB . What is the intensity of this sound wave?
(A) $6.0 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{2}$
(B) $1.0 \times 10^{-4} \mathrm{~W} / \mathrm{m}^{2}$
(C) $6.0 \times 10^{-4} \mathrm{~W} / \mathrm{m}^{2}$
(D) $1.0 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{2}$
(E) $1.0 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2}$

The speed of sound in air depends upon
(A) frequency
(B) wavelength
(C) amplitude
(D) speed of the sound source
(E) temperature of the air

Two sound waves have the same frequency. One of the sound waves is traveling in air at $331 \frac{\mathrm{~m}}{\mathrm{~s}}$ and the other is traveling in water at $1450 \frac{\mathrm{~m}}{\mathrm{~s}}$. What is the ratio of the wavelength of the sound in water to the wavelength of sound in air?
(A) 0.228
(B) 0.478
(C) 1.00
(D) 2.09
(E) 4.38

$432-\mathrm{Hz}$ tuning fork is the lowest frequency tuning fork that can produce resonance when held over one end a certain plastic tube open at both ends. When one end of this tube is closed, which of the following tuning fork frequencies would produce resonance when held over the open end?
(A) 133 Hz
(B) 288 Hz
(C) 720 Hz
(D) 1080 Hz
(E) 1296 Hz

A submarine emits a sonar signal to detect the distance to, and velocity of, a second nearby submarine. Which pair of wave behaviors is most closely associated with these two measurements?
(A) Absorption and Interference
(B) Diffraction and Refraction
(C) Dispersion and Polarization
(D) Reflection and Doppler Effect
(E) Refraction and Resonance

A transverse standing wave containing four loops is created on a string that is fixed at both ends. The string has a linear density $\mu$. A second string with the same length and a linear density of $4 \mu$ now replaces the first string. When placed under the same tension and vibrated at the same frequency, the standing wave produced on the second string will contain ...
(A) 1 loop.
(B) 2 loops.
(C) 4 loops.
(D) 8 loops.
(E) 16 loops.

The transverse wave shown on the right is traveling from left to right in a string. The direction of the velocity of the string at point $P$ is:
(A) left
(B) right
(C) up
(D) down
(E) unknown

A waterproof speaker placed at the bottom of a swimming pool emits a sound wave that travels toward the surface of the water. In the water, the sound wave has a frequency, $f_{\text {water }}$, a wavelength, $\lambda_{\text {water }}$, and wave speed, $v_{\text {water }}$. When the sound wave enters the air, it has a frequency, $f_{\text {air }}$, a wavelength, $\lambda_{\text {air }}$, and wave speed, $v_{\text {air }}$. Which one of the following relationships correctly compares the frequencies, wavelengths, and wave speeds of the waves in the air and water?
(A) $f_{\text {water }}=f_{\text {air }}$, $\lambda_{\text {water }}=\lambda_{\text {air }}$, $v_{\text {water }}=v_{\text {air }}$
(B) $f_{\text {water }}=f_{\text {air }}$, $\lambda_{\text {water }}>\lambda_{\text {air }}$, $v_{\text {water }}>v_{\text {air }}$
(C) $f_{\text {water }}<f_{\text {air }}$, $\lambda_{\text {water }}>\lambda_{\text {air }}$, $v_{\text {water }}=v_{\text {air }}$
(D) $f_{\text {water }}<f_{\text {air }}$, $\lambda_{\text {water }}=\lambda_{\text {air }}$, $v_{\text {water }}<v_{\text {air }}$
(E) $f_{\text {water }}=f_{\text {air }}$, $\lambda_{\text {water }}<\lambda_{\text {air }}$, $v_{\text {water }}>v_{\text {air }}$