To solve this problem, we need to understand the relationship between the speed of a wave, its frequency, and its wavelength. The formula that connects these three quantities is given by:
\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \]
Where:
- Speed is the speed of sound (in meters per second, m/s)
- Frequency is the frequency of the sound wave (in hertz, Hz)
- Wavelength is the distance between two consecutive points in phase on the wave (in meters, m)
We can rearrange this formula to solve for the wavelength if we have the speed of the wave and its frequency. The rearranged formula is:
\[ \text{Wavelength} = \frac{\text{Speed}}{\text{Frequency}} \]
Given:
- Speed of sound = 342 m/s
- Frequency of the sound wave = 50 Hz
We can now plug these values into the formula to calculate the wavelength:
\[ \text{Wavelength} = \frac{342 \text{ m/s}}{50 \text{ Hz}} \]
When calculating this, remember that Hz is equivalent to 1/s, so the units will work out to be in meters:
\[ \text{Wavelength} = \frac{342}{50} \text{ m} \]
\[ \text{Wavelength} = 6.84 \text{ m} \]
Final Answer:
The wavelength of a sound wave with a frequency of 50 Hz, when the speed of sound is 342 m/s, is 6.84 meters.
