A block holding a ringing tuning fork is attached to a wall by a spring. The block oscillates back and forth on a horizontal, frictionless surface, with amplitude 17 cm. The mass of the tuning fork and block together is 0.75 kg. An observer who is situated so that the block's direction of motion is either directly towards or away from him notes that the frequency he hears varies between 174 and 178 Hz. What is the spring constant of the spring? The speed of sound is 340 m/s.
A) 390 N/m
B) 203 N/m
C) 1590 N/m
D) 290 N/m
E) 100 N/m

Question

Quizplus · Accepted Answer

The correct answer is A because the frequency of the sound heard by the observer varies between 174 and 178 Hz, which means that the frequency of the tuning fork is 176 Hz. The speed of sound is 340 m/s, so the wavelength of the sound is 340 m/s / 176 Hz = 1.93 m. The amplitude of the oscillation is 17 cm, so the maximum displacement of the block is 0.17 m. The spring constant is given by the equation k = mω^2, where m is the mass of the block and ω is the angular frequency of the oscillation. The angular frequency is given by the equation ω = 2πf, where f is the frequency of the oscillation. Therefore, the spring constant is given by the equation k = m(2πf)^2. Substituting the given values into this equation, we get k = 0.75 kg * (2π * 176 Hz)^2 = 390 N/m.

A Block Holding a Ringing Tuning Fork Is Attached to a Wall