Question

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork. the vibrating length of wire ______.

Options

• should be same

• should be increased

• should be decreased

• should be 3 times the original length

Answer 1

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork. the vibrating length of wire should be decreased.

Explanation:

At equator mass of wire is more as compared to that at the poles.

Now, frequency of vibration of wire

f = `1/"2L" sqrt("T"/"m")`

⇒ `"f" prop 1/("L" sqrt"m")`

To achieve resonance with the same fork, the mass of the fork must be the same. At the equator, the wire is thicker. As a result, the vibrating length should be cut back.