Waves — Practice

Question 1

A 1 m string (mu = 0.01 kg/m, T = 100 N) is fixed at both ends. Find the fundamental frequency.

Accepted Answer

v = sqrt(T/mu) = sqrt(100/0.01) = 100 m/s. f1 = v/2L = 100/2 = 50 Hz.

Question 2

Waves y1 = 0.05 sin(200t - 5x) and y2 = 0.05 sin(200t + 5x) superpose. Find the standing wave and node positions.

Accepted Answer

y = 0.1 sin(5x) cos(200t). Nodes where sin(5x) = 0, i.e. x = n pi/5 (n = 0, 1, 2, ...).

Question 3

A source moving at 30 m/s emits 500 Hz toward a stationary observer (v = 340 m/s). Find the apparent frequency.

Accepted Answer

f' = fv/(v - v_s) = 500 x 340/(340 - 30) = 170000/310 = 548.4 Hz.

Question 4

Find the third harmonic of a 50 cm open organ pipe (v = 340 m/s).

Accepted Answer

f3 = 3v/2L = 3 x 340/(2 x 0.5) = 1020 Hz.

Question 5

Two tuning forks of 256 Hz and 260 Hz sound together. Find the beat frequency.

Accepted Answer

f_beat = |260 - 256| = 4 Hz, so 4 loudness maxima are heard per second.

Practice — Waves