a string 180 cm long resonates in a standing wave that has 3 segments when driven by a 270hz vibrator. What is the speed of the waves on the string?
(answer in book 324 m/s)
frequency = 270 hz
segments of wave = 3
v= f x wave
I don't know what to do.... help....thanks
The 3 segments of the wave means that there are 3 crests indicating that the length of the string is actually 3/2 of 1 wavelength or:
Wavelength=(Length)*(2/3)
Yes
f=270Hz,segment of wave=3,length of string=180cm,wavelength=180*(2/3)=73cm,velocity =270*72
Well, it seems you're in quite a "string" of confusion. But don't worry, I'm here to help, even if I have to stretch a few funny bones. Let's untangle this situation together, shall we?
Given that the string has 3 segments and a frequency of 270 Hz, we can determine the wavelength of the standing wave. In a standing wave, the number of segments would be equal to half of the number of wavelengths. So, in this case, we have 3 segments, which means we have 1.5 wavelengths.
Now, let's find the speed of the waves on the string. The speed (v) of a wave can be calculated by multiplying the frequency (f) by the wavelength (λ). In this case, the frequency is 270 Hz, and we need to find the wavelength.
Since we have 1.5 wavelengths, we can divide the length of the string (180 cm) by the number of wavelengths (1.5) to get the wavelength (λ). Mathematically, it would be:
Wavelength (λ) = Length of the string / Number of wavelengths
λ = 180 cm / 1.5
λ = 120 cm
Now that we have the wavelength (λ) and the frequency (f), we can find the speed (v) using the formula:
v = f x λ
v = 270 Hz × 120 cm
Converting the length from cm to meters:
v = 270 Hz × 1.2 m
v = 324 m/s
And there you have it! The speed of the waves on the string is indeed 324 m/s, just like the book said. I hope I was able to "string" the information together in an understandable way. If you have any more questions, feel free to let me know!
To find the speed of the waves on the string, you need to use the equation v = f * λ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.
First, let's find the wavelength of the standing wave on the string. Since the string has 3 segments, it means that there are 3 nodes (points of no displacement) in the wave. We know that the length of the string is 180 cm, but each segment only covers a portion of that length.
To find the length of each segment, divide the total length by the number of segments:
Length of each segment = Total length / Number of segments = 180 cm / 3 = 60 cm
Now, let's find the wavelength. The wavelength is twice the length of each segment because it consists of one complete crest and one complete trough. So:
Wavelength = 2 * Length of each segment = 2 * 60 cm = 120 cm
To convert the wavelength to meters, divide by 100:
Wavelength = 120 cm / 100 = 1.2 m
Finally, substitute the frequency and wavelength values into the equation v = f * λ:
v = 270 Hz * 1.2 m = 324 m/s
Therefore, the speed of the waves on the string is indeed 324 m/s, as stated in the book.