The question asks us to find the wavelength of a sound wave. We are given the wave's speed and information about how many crests and troughs it produces over a specific period.
Here's the information provided:
To find the wavelength, we first need to determine the frequency (\(f\)) of the sound wave. A complete wave cycle includes one crest and one trough. Therefore, observing 20 crests and 20 troughs means that 20 full wave cycles have occurred within the given time.
The formula for frequency is the number of waves (or cycles) divided by the time taken:
\(f = \frac{\text{Number of waves}}{\text{Time taken}}\)
Using the given values:
Number of waves = 20
Time taken, \(t = 0.1\) s
Now, we calculate the frequency:
\(f = \frac{20}{0.1 \text{ s}}\)
\(f = 200\) Hz
So, the frequency of the sound wave is 200 Hertz.
We know the relationship between the speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) of a wave is given by the formula:
\(v = f \lambda\)
To find the wavelength (\(\lambda\)), we can rearrange this formula:
\(\lambda = \frac{v}{f}\)
Now, we substitute the known values into the equation:
Speed, \(v = 330\) m/s
Frequency, \(f = 200\) Hz
\(\lambda = \frac{330 \text{ m/s}}{200 \text{ Hz}}\)
Calculating the result:
\(\lambda = \frac{33}{20}\) m
\(\lambda = 1.65\) m
Thus, the wavelength of the sound wave is 1.65 m.
Which of the following statements for persons suffering from presbyopia is/are correct?
1. They cannot distinguish colours.
2. It usually develops with ageing.
3. They wear either bi-focal lenses consisting of both concave and convex lenses or progressive lenses.
Select the answer using the code given below :
Which one among the following components is used as an amplifying device?
How long will a sound wave take to travel 1.5km, which has a frequency of 5 kHz and wavelength of 6 cm?
Which phenomenon is responsible for the echo of sound wave?
We hear an echo due to