PHYS 2211 Module 15 Self Assessment Practice Problems

15.1
Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air to its wavelength in seawater? Assume air temperature is 20.0°C.
Answer: 0.223

15.2
The displacement of the air molecules in sound wave is modeled with the wave function s(x,t) = 5.00 nm cos(91.54 m⁻¹x − 3.14 x 10⁴ s⁻¹t).
(a) What is the wave speed of the sound wave?
(b) What is the maximum speed of the air molecules as they oscillate in simple harmonic motion?
(c) What is the magnitude of the maximum acceleration of the air molecules as they oscillate in simple harmonic motion?
Answer: (a) 343 m/s (b) 1.57 x 10⁵ nm/s (c) 4.93 x 10⁹ nm/s²

15.3
A 250-Hz tuning fork is struck and begins to vibrate. A sound-level meter is located 34.00 m away. It takes the sound Δt = 0.10 s to reach the meter. The maximum displacement of the tuning fork is 1.00 mm. Write a wave function for the sound.
Answer: s(x,t) = 1 mm cos (4.62 m^-1 x – 1571 s^-1 t)

15.4
During a 4th of July celebration, an M80 firework explodes on the ground, producing a bright flash and a loud bang. The air temperature of the night air is T_F = 95.00°F. Two observers see the flash and hear the bang. The first observer notes the time between the flash and the bang as 0.10 second. The second observer notes the difference as 0.15 seconds. The line of sight between the two observers meet at a right angle as shown. What is the distance ∆x between the two observers?
Answer: 63.4 m

15.4

During a 4th of July celebration, an M80 firework explodes on the ground, producing a bright flash and a loud bang. The air temperature of the night air is T_F = 95.00°F. Two observers see the flash and hear the bang. The first observer notes the time between the flash and the bang as 0.10 second. The second observer notes the difference as 0.15 seconds. The line of sight between the two observers meet at a right angle as shown. What is the distance ∆x between the two observers?

Answer: 63.4 m

15.5
The warning tag on a lawn mower states that it produces noise at a level of 91.0 dB. What is the intensity of this sound in watts per meter squared?
Answer: 1.26 × 10⁻³ W/m²

15.6
Consider an idealized bird (treated as a point source) that emits constant sound power, with intensity obeying the inverse-square law. If you move twice the distance from the bird, by how many decibels does the sound intensity level drop?
Answer: 6 dB

15.7
Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away.
(a) At what distance d will the sound from the speakers first produce destructive interference at the listener’s location?
(b) If A is moved even farther away than in part (a), at what distance d will the speakers next produce destructive interference at the listener’s location?
(c) After A starts moving away from its original spot, at what distance d will the speakers first produce constructive interference at the listener’s location?
Answer: (a) 0.237 m (b) 0.710 m (c) 0.473 m

15.8
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from A. What is the closest you can be to B and be at a point of destructive interference?
Answer: 9 m

15.9
A commuter train blows its 200-Hz horn as it approaches a crossing. The speed of sound is 335 m/s.
(a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train?
(b) What frequency does the observer receive as the train moves away?
Answer: (a) 12.9 m/s (b) 193 Hz

15.10
On the planet Arrakis a male ornithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 Hz. If the stationary female hears a tone of 1240 Hz, what is the speed of sound in the atmosphere of Arrakis?
Answer: 861 m/s