For a certain transverse wave, the distance between two successive crests is 1.89 m, and 5 crests pass a given point along the direction of travel every 12.84 s. Calculate the wave speed.
The information you have been given allows you to calculate the frequency and the wavelength. In fact, they have told you what the wavelength is already.
The period is P = 12.85/5 = 2.57 s and the frequency is 1/P = ___ s^-1.
The product of wavelength and frequency is the wave speed.
That should enable you to do the calculation.
To calculate the wave speed, we need to use the formula:
Wave speed = Frequency x Wavelength
In this case, the wavelength is the distance between two successive crests, which is given as 1.89 m.
To find the frequency, we need to determine how many crests pass a given point in a given time period. In this case, it is stated that 5 crests pass a given point every 12.84 s.
To find the frequency, we can divide the number of crests (5) by the time period (12.84 s):
Frequency = 5 / 12.84 s
Now, we can substitute the values into the wave speed formula:
Wave speed = Frequency x Wavelength
Wave speed = (5 / 12.84 s) x 1.89 m
Calculating this, we find the wave speed to be approximately 0.736 m/s.