Question

When a stretched wire and tuning fork are sounded together 5 beats per second are produced, when length of wire is 95cm or 100 cm. frequency of fork is?

Answer 1

Tunning fork are sounded together 5 beats per second are produced or 5Hz.
Let frequency of fork = ν
then, probably frequencies of tunning fork due to beats formation are (ν + 5)Hz and (v - 5)Hz .
We know,
Frequency is inversely proportional to length of wire
∴ (ν + 5)/(v - 5) = 100/95
⇒95(v + 5) = 100(v - 5)
⇒19(v + 5) = 20(v - 5)
⇒19v + 95 = 20v - 100
⇒ 95 + 100 = 20v - 19v
⇒ 195 = v

Hence, frequency of fork = 195 Hz