The fundamental resonance on a string is 60 cm length fixed at both ends is 440Hz. What is the speed of a wave traveling on this string?
Think about it. One wavelength is 60 cm.
It takes 1/440 sec to travel the length of the string.
speed = d/t = d*f = 60*440 = 2640 cm/s
Hmm. Forgot the fundamental wavelength is 120cm, not 60.
scale the velocity to account for that.
To find the speed of a wave traveling on the string, we can use the equation:
v = f * λ
where:
v is the wave speed,
f is the frequency of the wave, and
λ is the wavelength of the wave.
In this case, we are given the fundamental frequency of the string as 440Hz. To find the wavelength (λ), we need to determine the length of the string.
The wavelength (λ) of the fundamental resonance mode can be calculated using the formula:
λ = 2L
where:
λ is the wavelength,
L is the length of the string.
Here, the length (L) of the string is given as 60 cm, so we can substitute this value into the equation:
λ = 2 * L
= 2 * 60 cm
= 120 cm
Now that we have the wavelength (λ) and the frequency (f), we can substitute these values into the wave speed equation:
v = f * λ
= 440 Hz * 120 cm
≈ 52800 cm/s
Therefore, the speed of the wave traveling on the string is approximately 52800 cm/s.