if an observer standing between 2 cliffs receives at 1.5sand 4s after clipping,find the distance between the cliffs if the velocity of sound is 320m/s

To find the distance between the two cliffs based on the time it takes for sound to travel back to the observer, we can break down the problem step by step. The observer hears the sound from the first cliff at 1.5 seconds and from the second cliff at 4 seconds. This means that the sound travels to the cliffs and back to the observer, so we need to consider the total distance traveled by the sound.

Understanding the Problem

When the observer claps, the sound travels to the first cliff and reflects back, and then it travels to the second cliff and returns. The times given (1.5 seconds and 4 seconds) represent the total time for the sound to make these round trips.

Calculating Distances

We can use the formula for distance, which is:

• Distance = Speed × Time

Given that the speed of sound is 320 m/s, we can calculate the distances for each cliff:

Distance to the First Cliff

For the first cliff, the time taken is 1.5 seconds:

• Distance to the first cliff = Speed × Time = 320 m/s × 1.5 s = 480 m

This distance (480 m) is the total distance for the sound to travel to the first cliff and back, so the distance to the cliff is half of this:

• Distance to the first cliff = 480 m / 2 = 240 m

Distance to the Second Cliff

For the second cliff, the time taken is 4 seconds:

• Distance to the second cliff = Speed × Time = 320 m/s × 4 s = 1280 m

Similarly, this distance is also for the round trip, so the distance to the second cliff is half of this:

• Distance to the second cliff = 1280 m / 2 = 640 m

Finding the Distance Between the Cliffs

Now that we have the distances to each cliff, we can find the distance between the two cliffs by subtracting the distance to the first cliff from the distance to the second cliff:

• Distance between the cliffs = Distance to the second cliff - Distance to the first cliff
• Distance between the cliffs = 640 m - 240 m = 400 m

Final Result

Thus, the distance between the two cliffs is 400 meters.

This method of using the speed of sound and the time taken for sound to travel is a practical application of basic physics principles, demonstrating how we can measure distances using sound waves. If you have any further questions or need clarification on any part of this process, feel free to ask!