If the fundamental frequency for a 60-cm long guitar string is 500 Hz, what is the speed of the traveling waves?
The speed of the traveling waves is 340 m/s.
To find the speed of the traveling waves on a guitar string, we can use the formula:
v = f * λ
where:
- v represents the speed of the wave
- f is the frequency of the wave
- λ symbolizes the wavelength
In this case, we know the fundamental frequency (f) of the 60-cm long guitar string is 500 Hz.
To calculate the wavelength (λ) of the wave, we can use the formula:
λ = 2L/n
where:
- L is the length of the string
- n is the harmonic number
Since we are dealing with the fundamental frequency (first harmonic), n = 1.
Plugging in the known values:
L = 60 cm
n = 1
λ = 2 * 60 cm / 1 = 120 cm
Now, we can substitute the values of f and λ into the first equation to calculate the speed (v) of the traveling waves:
v = 500 Hz * 120 cm = 60,000 cm/s
Therefore, the speed of the traveling waves on the 60-cm long guitar string is 60,000 cm/s.
To find the speed of the traveling waves on a guitar string, we can use the formula:
v = f * λ
where v is the speed of the waves, f is the frequency, and λ is the wavelength.
In this case, we are given the fundamental frequency of 500 Hz and the length of the guitar string, which is 60 cm. The fundamental frequency corresponds to the first harmonic, which has a wavelength that is twice the length of the string.
λ = 2 * L = 2 * 60 cm = 120 cm = 1.2 m
Now we can substitute the values into the formula:
v = 500 Hz * 1.2 m
v = 600 m/s
Therefore, the speed of the traveling waves on the guitar string is 600 m/s.