A 2.2 m-long string is fixed at both ends and tightened until the wave speed is 50 m/s.What is the frequency of the standing wave shown in the figure?
picture has 6 waves
Count the cycles. From equilibrium up to the crest, down the trough, and back to equilibrium (like a complete sinusoidal wave)--that is one cycle.
Find the time: the distance of the string, divide it by the speed. This is the basic concept of velocity=displacement/time. You just solve for time.
You have seconds and you have cycles. What is frequency? Cycles per second. There.
If it is truly six waves, then the 2.2m is six wavelengths long.
f*Lambda=50
how did you arrive at 50 because picture might have 7 nodes
50 was given as wavespeed.
I cant determine how many wavelengths the string is, you will have to do that.
but how do i do it
Well, it seems like you're in quite a wave-y situation! Let's figure out the frequency of this standing wave.
First, we need to find the wavelength of the wave. From the picture you provided, we can see that there are 6 waves along the 2.2 m length of the string. So, the wavelength would be the total length divided by the number of waves, which gives us 2.2 m / 6 waves = 0.3667 m.
Now, let's recall the formula that relates the wave speed (v), wavelength (λ), and frequency (f): v = λ * f.
We know that the wave speed is 50 m/s, and we found the wavelength to be 0.3667 m. So, we can rearrange the formula to solve for the frequency:
f = v / λ = 50 m/s / 0.3667 m = 136.3 Hz.
So, the frequency of the standing wave in the figure is approximately 136.3 Hz. Keep up the good vibrations!
To find the frequency of the standing wave, we need to first count the number of waves in the picture provided. You mentioned that there are 6 waves.
The total distance covered by these 6 waves is the length of the string, which is given as 2.2 meters.
Since each wave consists of one complete cycle (crest to crest or trough to trough), the total distance covered by the 6 waves is equal to the wavelength of the wave.
Therefore, the wavelength (λ) is equal to the total distance (2.2 meters) divided by the number of waves (6):
λ = 2.2 meters / 6 waves
Now that we have the wavelength, we can calculate the frequency (f) using the wave speed (v) and the wavelength.
The wave speed is given as 50 m/s.
We know that the wave speed (v) is equal to the product of the wavelength (λ) and the frequency (f):
v = λ * f
Rearranging the equation, we can solve for the frequency (f):
f = v / λ
Substituting the values, we have:
f = 50 m/s / (2.2 meters / 6 waves)
Simplifying the equation gives us:
f = 50 m/s * (6 waves / 2.2 meters)
f ≈ 136.36 Hz
Therefore, the frequency of the standing wave shown in the figure is approximately 136.36 Hz.