Question

38. A 1024 Hz tuning fork is dangled at the end of a string such that its center of mass is 1.2 m below the point at which the other end of the string is attached to door frame, making a pendulum of sorts. The tuning fork may be treated as a point mass for the purposes of this problem. The pendulum is brought to a maximum angle and released. If the range of frequencies heard by an observer standing in the plane of the pendulum's motion is 1020-1028 Hz, what is the angle to which the pendulum was raised? The speed of sound is 340 m/s.

• 17°

• 22°

• 18°

• 4.3°

• 46°

Answer 1

22 degrees is the correct answer.

let v = 340 m/s

let v_source is the speed of tuning fork when it moves towards the observer.

f = 1024 Hz
f' = 1028 Hz

Using doppler's equation, f' = f*v/(v - v_source)

v - v_source = f*v/f'

v_source = v - f*v/f'

= 340 - 1024*340/1028

= 1.323 m/s

let h is the height raised by the pendulum.

v_source = sqrt(2*g*h)

==> h = v_source^2/(2*g)

= 1.323^2/(2*9.8)

= 0.0893 m

if theta is athe angle raised,

h = L*(1 - cos(theta))

h/L = 1 -cos(theta)

cos(theta) = 1 - h/L

= 1 - 0.0893/1.2

= 0.9256

theta = cos^-1(0.9256)

= 22 degrees <<<<<<<<<<<<-----------------------------Answer