The fundamental frequency of a standing wave on a 1.0 m long string is 440 Hz. What would be the wave speed of a pulse moving along the string
To find the wave speed of a pulse moving along a string, you need to use the equation:
Wave speed (v) = Frequency (f) × Wavelength (λ)
In this case, we are given the fundamental frequency, f = 440 Hz. However, we still need to find the wavelength.
The wavelength (λ) of a standing wave on a string is related to the length of the string by the equation:
Wavelength (λ) = 2 * Length (L)
Given that the length of the string is 1.0 m, we can calculate the wavelength:
Wavelength (λ) = 2 * 1.0 m = 2.0 m
Now we can substitute the values into the equation for wave speed:
Wave speed (v) = 440 Hz * 2.0 m
Wave speed (v) = 880 m/s
Therefore, the wave speed of the pulse moving along the string is 880 m/s.
To determine the wave speed of a pulse moving along a string, we need to understand the relationship between the wave speed, frequency, and wavelength.
The relationship is given by the formula:
Wave speed (v) = Frequency (f) × Wavelength (λ)
In this case, we are given the fundamental frequency of the standing wave, which is 440 Hz. The fundamental frequency is the lowest frequency at which the string can vibrate.
Knowing the fundamental frequency alone is not sufficient to directly determine the wave speed. However, we also need to consider the length of the string.
In a standing wave on a string, the fundamental frequency corresponds to a wavelength that is twice the length of the string (λ = 2L), where L is the length of the string.
So, in this case, the wavelength can be calculated as:
Wavelength (λ) = 2 × Length of the string = 2 × 1.0 m = 2.0 m
Now, we can substitute the given values of frequency and wavelength into the formula to find the wave speed:
Wave speed (v) = Frequency (f) × Wavelength (λ)
v = 440 Hz × 2.0 m
Solving this equation, we can find the wave speed:
v = 880 m/s
Therefore, the wave speed of the pulse moving along the string is 880 m/s.
T = (1/440) in seconds
fundamental is half a wavelength in length of string (nodes at the two fixed ends)
so wavelength = 2.0 meters
v = distance / time = 2.0 * 440 = 880 m/s