AP Physics Practice Questions: Waves & Sound

AP Physics multiple choice questions on wave properties, sound, and interference. Each question includes detailed solutions at the bottom of the page.

1. A transverse wave on a string is described by y = 0.02 sin(30x - 400t) where all quantities are in SI units. What is the speed of the wave?

   A) 7.5 m/s
   B) 13.3 m/s
   C) 15.0 m/s
   D) 30.0 m/s
   E) 40.0 m/s

2. Two speakers 3.0 m apart emit identical 340 Hz sound waves in phase. A listener stands 4.0 m directly in front of one speaker. What is the phase difference at the listener's position?

   A) 0°
   B) 90°
   C) 180°
   D) 270°
   E) 450°

3. A string fixed at both ends is 1.5 m long. The third harmonic has frequency 180 Hz. What is the wave speed on the string?

   A) 60 m/s
   B) 90 m/s
   C) 120 m/s
   D) 180 m/s
   E) 270 m/s

4. A police car with siren frequency 800 Hz approaches a stationary observer at 30 m/s. What frequency does the observer hear? (Speed of sound = 340 m/s)

   A) 732 Hz
   B) 800 Hz
   C) 876 Hz
   D) 924 Hz
   E) 960 Hz

5. Two point sources emit waves of wavelength λ. At what angles (from the central maximum) will constructive interference occur?

   A) sinθ = mλ/d
   B) sinθ = (m+½)λ/d
   C) sinθ = mλ
   D) sinθ = λ/d
   E) sinθ = d/λ

Solutions

1. B) 13.3 m/s
   Wave equation: \(y = A \sin(kx - \omega t)\)
   \(k = 30\ \text{rad/m}, \ \omega = 400\ \text{rad/s}\)
   \(v = \frac{\omega}{k} = \frac{400}{30} \approx 13.33\ \text{m/s}\)

2. A) 0°
   Path difference: \(\Delta r = \sqrt{4^2 + 3^2} - 4 = 5 - 4 = 1.0\ \text{m}\)
   Wavelength: \(\lambda = \frac{v}{f} = \frac{340}{340} = 1.0\ \text{m}\)
   Phase difference: \(\Delta \phi = \frac{\Delta r}{\lambda} \times 360^\circ = \frac{1.0}{1.0} \times 360^\circ = 360^\circ\)
   But \(360^\circ\) is equivalent to \(0^\circ\) phase difference.

3. D) 180 m/s
   For a string fixed at both ends: \(f_n = \frac{n v}{2 L}\), where \(n =\) harmonic number
   Third harmonic: \(n = 3\), so \(f_3 = \frac{3 v}{2 L}\)
   \(v = \frac{2 L f_3}{3} = \frac{2 \times 1.5 \times 180}{3} = \frac{540}{3} = 180\ \text{m/s}\)

4. C) 876 Hz
   Doppler effect: \(f' = f \frac{v}{v - v_s}\), where \(v_s\) is the source speed
   \(f' = 800 \times \frac{340}{340 - 30} = 800 \times \frac{340}{310} \approx 800 \times 1.0968 \approx 877.4\ \text{Hz} \approx 876\ \text{Hz}\)

5. A) \(\sin\theta = \frac{m \lambda}{d}\)
   For constructive interference from two slits/sources: \(d \sin\theta = m \lambda\)
   Therefore, \(\sin\theta = \frac{m \lambda}{d}\)