The mass of a string is 6.0 x 10^-3 kg, and it is stretched so the tension in it is 195 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?
To find the length of the string, we can use the formula for the speed of a wave on a string:
speed of wave = frequency * wavelength
Given:
Frequency (f) = 260 Hz
Wavelength (λ) = 0.60 m
We can substitute these values into the formula:
speed of wave = 260 Hz * 0.60 m
The speed of a wave on a string depends on the tension in the string and the mass per unit length of the string. The formula for the speed of a wave on a string is:
speed of wave = √(tension / mass per unit length)
To find the mass per unit length, we can rearrange the above formula:
mass per unit length = tension / (speed of wave)^2
Given:
Tension (T) = 195 N
We can calculate the mass per unit length:
mass per unit length = 195 N / (speed of wave)^2
Now, we can substitute the calculated mass per unit length into the formula for the speed of the wave:
speed of wave = √(195 N / mass per unit length)
Finally, we can substitute the calculated speed of the wave back into the original formula to find the length of the string:
length of string = speed of wave / frequency
Now, let's calculate everything step by step:
1. Calculate the mass per unit length:
mass per unit length = 195 N / (speed of wave)^2
2. Calculate the speed of the wave:
speed of wave = √(195 N / mass per unit length)
3. Calculate the length of the string:
length of string = speed of wave / frequency
By following these steps, you can find the length of the string.