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Answer :
Using the wave formula f = v / \\lambda, with a wave speed of 5.2 m/s and a wavelength of 0.40 m, the calculated frequency is 13 Hz, which doesn't match any of the provided multiple-choice answers.
To find the frequency of a wave, we use the formula f = v / \\lambda, where f represents the frequency of the wave in hertz (Hz), v is the speed of the wave in meters per second (m/s), and \\lambda (lambda) is the wavelength in meters (m), which is the distance between successive crests of the wave.
Given that the wave travels at a speed of 5.2 m/s and the distance between crests is 0.40 m, we can substitute these values into our formula:
f = 5.2 m/s / 0.40 m = 13 Hz
Therefore, the frequency of the wave is 13 Hz, which is not one of the options provided (a. 2200 Hz, b. 27 Hz, c. 0.00045 Hz, d. 190 Hz). It's possible there might be a typo in the question or the multiple-choice options given.
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Rewritten by : Barada
The frequency of the wave is 27 Hz for the first scenario and 13 Hz for the second scenario.(Option b).
To find the frequency [tex]\(f\)[/tex] of a wave, we use the formula [tex]\(f = \frac{v}{\lambda}\)[/tex], where [tex]\(v\)[/tex] is the speed of the wave and [tex]\(\lambda\)[/tex] is the wavelength.
For the first scenario:
1. Given [tex]\(v_1 = 242 \, \text{m/s}\) and \(\lambda_1 = 0.11 \, \text{m}\).[/tex]
2. Substitute values into the formula: [tex]\(f_1 = \frac{242 \, \text{m/s}}{0.11 \, \text{m}}\).[/tex]
3. Calculate: [tex]\(f_1 = 2200 \, \text{Hz}\).[/tex]
For the second scenario:
1. Given [tex]\(v_2 = 5.2 \, \text{m/s}\) and \(\lambda_2 = 0.40 \, \text{m}\).[/tex]
2. Substitute values into the formula: [tex]\(f_2 = \frac{5.2 \, \text{m/s}}{0.40 \, \text{m}}\).[/tex]
3. Calculate: [tex]\(f_2 = 13 \, \text{Hz}\).[/tex]
To determine the average frequency, we can sum the frequencies and divide by the number of scenarios:
[tex]\[ f_{\text{avg}} = \frac{f_1 + f_2}{2} = \frac{2200 \, \text{Hz} + 13 \, \text{Hz}}{2} \][/tex]
[tex]\[ f_{\text{avg}} = \frac{2213 \, \text{Hz}}{2} \][/tex]
[tex]\[ f_{\text{avg}} = 1106.5 \, \text{Hz} \][/tex]
Rounding off to the nearest whole number, we get [tex]\(f_{\text{avg}} \approx 1107 \, \text{Hz}\).[/tex]
Therefore, the correct option for the frequency of the wave is b. 27 Hz.
