The length of the B string on a certain guitar is 60.0 cm. It vibrates at a fundamental frequency of 246.0 Hz. What is the speed of the transverse waves on the string?
To find the speed of the transverse waves on the string, we can use the formula:
v = λ * f
where v is the velocity/speed of the wave, λ is the wavelength, and f is the frequency.
In this case, we're given the frequency (f = 246 Hz), but we need to find the wavelength (λ) first.
The wavelength can be calculated using the formula:
λ = 2L
where L is the length of the string.
Given that the length of the string is 60.0 cm (L = 60.0 cm), we can substitute this value into the formula:
λ = 2 * 60.0 cm = 120.0 cm
Now, we have the wavelength (λ) and the frequency (f), so we can substitute these values into the velocity formula:
v = λ * f = 120.0 cm * 246.0 Hz
However, we need to convert the units to be consistent. Let's convert the cm to m since it's the SI unit for length:
1 cm = 0.01 m
Therefore, 120.0 cm = 1.20 m
Finally, we can calculate the speed of the transverse waves on the string:
v = 1.20 m * 246.0 Hz = 295.20 m/s
Therefore, the speed of the transverse waves on the B string is 295.20 m/s.