A stretched wire of 80cm vibrates with fundamental frequency of 256Hz.If length of wire is reduced to 15cm, the fundamental frequency now will be?
freq= k/length
freq*length=k
256*80cm=f*15dm
f=256*80/15 hz
To find the new fundamental frequency of the stretched wire when its length is reduced to 15 cm, we can use the formula:
f = v / λ
Where:
f is the frequency,
v is the velocity of the wave, and
λ (lambda) is the wavelength of the wave.
We know that the length of the stretched wire is related to the wavelength of the wave by the equation:
λ = 2L
Where L is the length of the wire.
Given:
The initial length of the wire is 80 cm, which means L = 80 cm = 0.8 m.
The initial fundamental frequency is 256 Hz.
The new length of the wire is 15 cm, which means L' = 15 cm = 0.15 m.
To find the new fundamental frequency, we need to calculate the new wavelength first:
λ' = 2L' = 2 * 0.15 = 0.3 m
Now, we can calculate the new frequency using the formula:
f' = v / λ'
Since the velocity of the wave remains constant, we can assume it remains the same as in the initial condition.
Therefore, the new fundamental frequency, f', can be calculated as:
f' = (v / λ) * λ' = (256 Hz) * (0.3 m / 0.8 m) = 96 Hz
So, when the length of the wire is reduced to 15 cm, the new fundamental frequency will be 96 Hz.