a sound wave of frequency 1.2hz is reflected from a barrier 75m away and its receiver 0.5 sec after transmission.calculate the wave length of the sound
To calculate the wavelength of the sound wave, you'll need to use the formula:
wavelength (λ) = speed of sound (v) / frequency (f)
Step 1: Calculate the speed of sound
The speed of sound in air at room temperature is approximately 343 meters per second.
Step 2: Calculate the time it takes for the sound wave to travel to the barrier and back.
Given that the receiver detects the sound 0.5 seconds after transmission, and assuming the sound wave travels directly to the barrier and back, we can divide this time by 2 to find the time it takes for the sound wave to reach the barrier.
Therefore, the time to reach the barrier would be 0.5 seconds divided by 2, which is 0.25 seconds.
Step 3: Calculate the distance traveled by the sound wave.
We know that the sound wave covers a distance of 75 meters (the distance to the barrier and back). This means the distance traveled to reach the barrier will be half of that, which is 75 meters divided by 2, resulting in 37.5 meters.
Step 4: Calculate the frequency.
The frequency given in the problem is 1.2 Hz.
Step 5: Now, plug the calculated values into the formula to find the wavelength.
wavelength (λ) = speed of sound (v) / frequency (f)
wavelength (λ) = 343 m/s / 1.2 Hz
wavelength (λ) ≈ 285.83 meters
Therefore, the wavelength of the sound wave is approximately 285.83 meters.