7) There are 5 successive compressions of a sound wave train in 7.20 cm. If the sound wave travels 6.80 km in 20.0 seconds.determine the frequency of the sound wave. (1.89times 10^4Hz)

Here's how to determine the frequency of the sound wave:<br /><br />1. **Wavelength Calculation:**<br /><br />Since there are 5 compressions in 7.20 cm, this represents 4 full wavelengths. (Think of it like the distance between 5 fence posts - there are only 4 spaces between them.) Therefore, the wavelength (λ) is:<br /><br />λ = 7.20 cm / 4 = 1.80 cm = 0.0180 m (It's important to convert to meters for consistency with other units)<br /><br />2. **Speed Calculation:**<br /><br />The speed (v) of the sound wave is given by the distance traveled divided by the time taken:<br /><br />v = 6.80 km / 20.0 s = 6800 m / 20.0 s = 340 m/s<br /><br />3. **Frequency Calculation:**<br /><br />The frequency (f) of a wave is related to its speed and wavelength by the following equation:<br /><br />v = fλ<br /><br />Solving for frequency:<br /><br />f = v / λ = 340 m/s / 0.0180 m = 18888.89 Hz<br /><br />4. **Rounding for Significant Figures:**<br /><br />The given values have three significant figures, so the final answer should also have three significant figures:<br /><br />f ≈ 1.89 x 10⁴ Hz<br /><br />Therefore, the frequency of the sound wave is approximately $\boxed{1.89 \times 10^4 Hz}$.<br />