A sound wave has a frequency of 3.5 kHz and wavelength 0.1 m. How long will it take to travel 700 m?
Understanding the Problem: Sound Wave Travel Time
The question asks us to determine the time it takes for a sound wave to travel a specific distance, given its frequency and wavelength. To solve this, we first need to find the speed of the sound wave using the provided frequency and wavelength. Then, we can use the constant speed formula to calculate the time taken to cover the given distance.
Key Information Provided:
| Property | Value |
|---|---|
| Frequency ($f$) | 3.5 kHz |
| Wavelength ($\lambda$) | 0.1 m |
| Distance ($d$) | 700 m |
Calculating the Speed of the Sound Wave
The speed ($v$) of a wave is related to its frequency ($f$) and wavelength ($\lambda$) by the equation:
$$\large v = f \lambda$$
First, let's convert the frequency from kilohertz (kHz) to hertz (Hz). 1 kHz = 1000 Hz.
$$\large f = 3.5 \text{ kHz} = 3.5 \times 1000 \text{ Hz} = 3500 \text{ Hz}$$
Now, we can calculate the wave speed:
$$\large v = (3500 \text{ Hz}) \times (0.1 \text{ m})$$
$$\large v = 350 \text{ m/s}$$
So, the speed of the sound wave is 350 meters per second.
Determining the Time to Travel 700 m
Now that we know the speed of the sound wave, we can calculate the time ($t$) it takes to travel a distance ($d$) using the formula:
$$\large t = \frac{d}{v}$$
We are given the distance $d = 700$ m and we calculated the speed $v = 350$ m/s.
$$\large t = \frac{700 \text{ m}}{350 \text{ m/s}}$$
$$\large t = 2 \text{ s}$$
Therefore, it will take 2 seconds for the sound wave to travel 700 m.
Conclusion
Based on the calculations, the time taken for the sound wave with a frequency of 3.5 kHz and wavelength 0.1 m to travel a distance of 700 m is 2.0 seconds.
Revision Table: Sound Wave Calculations
| Concept | Formula | Units |
|---|---|---|
| Wave Speed | $v = f \lambda$ | m/s |
| Time, Distance, Speed | $t = d/v$ | s |
| Frequency | $f$ | Hz (or kHz) |
| Wavelength | $\lambda$ | m |
| Distance | $d$ | m |
| Time | $t$ | s |
Additional Information: Properties of Sound Waves
Sound waves are mechanical waves that require a medium (like air, water, or solids) to travel. They are typically longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of wave propagation.
- Frequency: Determines the pitch of the sound. Higher frequency means higher pitch. Measured in Hertz (Hz).
- Wavelength: The distance between two consecutive points on a wave that are in the same phase (e.g., peak to peak). Measured in meters (m).
- Speed: How fast the wave energy travels through the medium. The speed of sound depends on the properties of the medium, such as temperature, density, and elasticity. For example, sound travels faster in solids than in liquids, and faster in liquids than in gases.
- Amplitude: Relates to the intensity or loudness of the sound. Higher amplitude means louder sound.
The relationship $v = f\lambda$ is fundamental for all types of waves, including sound waves, light waves, and water waves.
Important Questions from Wave
Which one of the following statements is true for sound waves propa- gating in air?
Which one of the following optical phenomena supports that the light is a transverse wave?
Which of the following is the horizontal distance between two successive crests?
Which of the following statements is correct?
What is the correct order of radiations in descending order of frequencies?
