The figure below shows a standing wave oscillating at 95 Hz on a string. The distance d between the two walls equals 70 cm. What is the wave speed?
pic have 3 waves
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To find the wave speed, we need to use the formula:
Wave speed (v) = frequency (f) x wavelength (λ)
In the given figure, it is mentioned that the standing wave oscillates at a frequency of 95 Hz. However, the wavelength is not directly given. We can find the wavelength by looking at the distance between the two walls (70 cm) and the number of waves within that distance.
Since the distance between two consecutive wave's crests or troughs is half a wavelength, we can count the number of crests or troughs within the given distance (d = 70 cm) in the figure. You mentioned that there are three waves, so there are three complete wavelengths within the distance d.
So, the number of wavelengths (n) is equal to the number of waves (3). The total distance covered by the three wavelengths is equal to the distance between the walls (d = 70 cm).
Therefore, the wavelength (λ) can be found by dividing the distance d by the number of wavelengths:
Wavelength (λ) = distance (d) / number of wavelengths (n)
Substituting the given values, we can calculate the wavelength:
Wavelength (λ) = d / n = 70 cm / 3 ≈ 23.3 cm
Now that we have the frequency (f = 95 Hz) and the wavelength (λ ≈ 23.3 cm), we can use the formula to find the wave speed (v):
Wave speed (v) = frequency (f) x wavelength (λ)
Substituting the given values:
Wave speed (v) = 95 Hz x 23.3 cm ≈ 2213.5 cm/s
Therefore, the wave speed is approximately 2213.5 cm/s.