JEE Physics Sound Waves MCQs Set 10

Answer: (b) 247.5 m

Explanation:
1. The sound travels to the hill and back: \( 2d = 330\times1.5 \).
2. \( d = 247.5 \) m.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) 33 m

Explanation:
1. Time for 36 vibrations \( = 36/384 \) s.
2. Distance \( = 352\times\frac{36}{384} = 33 \) m.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (c) \( y = 0.2\sin2\pi\left(6t-\frac x{60}\right) \)

Explanation:
1. \( f = v/\lambda = 360/60 = 6 \) Hz.
2. A wave in the \( +x \) direction is \( y = A\sin2\pi(ft-x/\lambda) = 0.2\sin2\pi\left(6t-\frac x{60}\right) \).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) \( \sqrt{A_1^2+A_2^2+2A_1A_2\cos(\beta_1-\beta_2)} \)

Explanation:
1. The phasor sum of two vibrations of phase difference \( \delta=\beta_1-\beta_2 \) has amplitude \( \sqrt{A_1^2+A_2^2+2A_1A_2\cos\delta} \).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) \( 72^\circ \)

Explanation:
1. \( k = 0.2\pi \) rad/cm.
2. \( \Delta\phi = k\Delta x = 0.2\pi\times2 = 0.4\pi \), i.e. \( 72^\circ \).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) v

Explanation:
1. The speed of sound depends on the medium, not on the frequency, so it stays v (the wavelength becomes one-fourth).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) 63 cm/s

Explanation:
1. \( \omega = 2\pi \) rad/s.
2. \( v_{max} = A\omega = 10\times2\pi = 62.8 \) cm/s.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) 2.0 Hz

Explanation:
1. \( \omega = 4\pi \Rightarrow f = \omega/2\pi = 2 \) Hz.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) \( \pi/2 \)

Explanation:
1. \( \lambda = v/f = 0.1 \) m.
2. \( \Delta\phi = \frac{2\pi}{\lambda}\Delta x = \frac{2\pi\times0.025}{0.1} = \frac\pi2 \).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) 20 mm

Explanation:
1. The highest audible frequency is about 20 kHz, so \( \lambda_{min} = 340/20000 \approx 1.7 \) cm, which is of the order of 20 mm.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) \( \lambda = \frac16 \) m and \( v = 250 \) m/s

Explanation:
1. \( k = 12\pi \Rightarrow \lambda = 2\pi/k = \frac16 \) m.
2. \( v = \omega/k = 3000\pi/12\pi = 250 \) m/s; the frequency is 1500 Hz.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (b) 16

Explanation:
1. \( v = \frac\omega k = \frac{\pi/2}{\pi/4} = 2 \) m/s.
2. Distance in 8 s \( = 16 \) m.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (c) 3 cm

Explanation:
1. \( k = \pi/3 \) cm\(^{-1}\), so \( \lambda = 6 \) cm.
2. Distance between consecutive nodes \( = \lambda/2 = 3 \) cm.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (d) 390 Hz

Explanation:
1. A is either 378 or 390 Hz.
2. Loading lowers the frequency of A. If A were 378 Hz the beats would increase, so A = 390 Hz (it falls to 388 Hz and gives 4 beats).

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (c) \( \frac18 \) s

Explanation:
1. The beat period is \( 1/4 \) s.
2. Maximum to the next minimum is half a beat period, \( \frac18 \) s.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) 200, 400

Explanation:
1. There are 40 intervals of 5 Hz, so \( f_{last}-f_{first} = 200 \) Hz.
2. With \( f_{last} = 2f_{first} \), \( f_{first} = 200 \) Hz and \( f_{last} = 400 \) Hz.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (b) 1.256 m

Explanation:
1. \( k = 5 \) m\(^{-1}\), so \( \lambda = \frac{2\pi}{5} = 1.256 \) m.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.

Answer: (a) 20 cm

Explanation:
1. \( k = \pi/20 \) cm\(^{-1}\), so \( \lambda = 40 \) cm.
2. Node spacing \( = \lambda/2 = 20 \) cm.

Teacher's Note:
1. Identify the wave parameters from the equation or the given data before substituting.
2. Check that the units of v, f and \( \lambda \) are consistent.