A stretched string of length 80 cm has a fundamental frequency of vibration of 400 Hz.
What is the speed of the sound wave in the stretched string?
The length of the string is 1/2 wavelength.
wavlength*frequency=speed of wave
To determine the speed of the sound wave in a stretched string, we need to use the formula:
v = f * λ,
where:
v is the velocity or speed of the sound wave,
f is the frequency of the vibration, and
λ (lambda) is the wavelength.
In this case, we are given the fundamental frequency of vibration (f = 400 Hz). However, we still need to find the wavelength (λ) before we can calculate the speed (v).
To determine the wavelength, we need to use the formula:
λ = 2L/n,
where:
L is the length of the string,
n is the mode or harmonic number.
In this case, we are given the length of the string (L = 80 cm) and we are looking for the fundamental frequency (n = 1), so we can substitute these values into the formula:
λ = 2 * 80 cm / 1 = 160 cm.
Now that we have the wavelength, we can calculate the speed of the sound wave by substituting the frequency and wavelength into the equation:
v = 400 Hz * 160 cm = 64,000 cm/s.
Therefore, the speed of the sound wave in the stretched string is 64,000 cm/s.