There is a 1.2 m distance between a crest and an adjacent trough in a series of waves on the surface of a lake. In 30s, 35 crests pass a buoy anchored in the lake. What is the speed of these waves?
The wavelength is the crest-to-crest distance, which would be 2.4 m.
Multiply that by frequency to get the wave speed.
The frequency is 35/30 = 1.17 Hz
1.2x2x34/30
Distance between two crest points is 1.2x2
Distance between 35 crest points is 1.2x2x34.
Note a crest is a point. One may not measure the time duration of a crest point.
I've just noted that waves and crests are both used in such problems. The total distance is commonly given by multiplying the number, or 35 in this case. To me, this is really confusing!
To find the speed of the waves, we can use the formula: speed = wavelength × frequency.
First, let's find the wavelength. The wavelength is the distance between two adjacent crests or troughs. We are given that the distance between a crest and an adjacent trough is 1.2 m. Since one complete wave consists of two crests or two troughs, the wavelength can be calculated as follows:
wavelength = 2 × distance between crest and trough = 2 × 1.2 m = 2.4 m.
Next, we need to find the frequency of the waves. The frequency is the number of crests passing by a given point in a given time, which is given as 35 crests in 30 seconds. The frequency can be calculated as follows:
frequency = number of crests ÷ time = 35 crests ÷ 30 s = 1.17 Hz (rounded to two decimal places).
Now we have both the wavelength (2.4 m) and the frequency (1.17 Hz). We can substitute these values into the formula to calculate the speed of the waves:
speed = wavelength × frequency = 2.4 m × 1.17 Hz = 2.808 m/s (rounded to three decimal places).
Therefore, the speed of these waves on the surface of the lake is approximately 2.808 m/s.