One end of a string 5.34 m long is moved up and down with simple harmonic motion at a frequency of 15 Hz . The waves reach the other end of the string in 0.5 s .
Find the wavelength of the waves on the
string. Answer in units of cm
frequency*wavelength=speed
In this case, speed is 5.34/.5 m/s
solve for wavelength.
To find the wavelength of the waves on the string, we can use the formula:
wavelength = speed / frequency
First, let's determine the speed of the waves on the string. We know that the waves reach the other end of the string in 0.5 seconds, and the length of the string is 5.34 meters. Thus, we can calculate the speed as follows:
speed = distance / time
speed = 5.34 m / 0.5 s
speed = 10.68 m/s
Now, we can substitute the given frequency and calculated speed into the wavelength formula:
wavelength = speed / frequency
wavelength = 10.68 m/s / 15 Hz
wavelength ≈ 0.712 m
Finally, to convert the wavelength to centimeters, we multiply by 100:
wavelength in cm = 0.712 m * 100 cm/m
wavelength ≈ 71.2 cm
Therefore, the wavelength of the waves on the string is approximately 71.2 cm.
To find the wavelength of the waves on the string, we can use the formula:
wavelength (λ) = wave speed (v) / frequency (f)
First, let's find the wave speed (v). We know that the waves reach the other end of the string in 0.5 seconds, and the string is 5.34 meters long. The wave speed is calculated by dividing the distance traveled by the time taken:
wave speed (v) = distance / time
v = 5.34 m / 0.5 s
v = 10.68 m/s
Now, we can substitute the wave speed (10.68 m/s) and frequency (15 Hz) into the wavelength formula:
wavelength (λ) = 10.68 m/s / 15 Hz
λ = 0.712 m
Finally, to convert the wavelength to centimeters, we multiply by 100 (since there are 100 centimeters in a meter):
λ = 0.712 m * 100 cm/m
λ = 71.2 cm
Therefore, the wavelength of the waves on the string is 71.2 cm.