Question

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.

Answer 1

The spring constant of the spring is 16,296.79 N/m.

Step-by-step explanation:

To find the spring constant of the spring, we can use the relationship between the frequency of the tuning fork and the spring constant. The formula for the frequency of an oscillating mass-spring system is given by:

f = (1 / 2π) * (k / m)^0.5

where f is the frequency, k is the spring constant, and m is the mass of the system. Rearranging the formula, we have:

k = (4π^2 * m * f^2)

Given that the mass of the tuning fork and block together is 0.75 kg and the observer hears a frequency range of 174 Hz to 178 Hz, we can substitute these values into the formula to calculate the spring constant:

k = (4π^2 * 0.75 * 174^2)

= 16,296.79 N/m

Therefore, the spring constant of the spring is approximately 16,296.79 N/m.