A hammer taps on the end of a 4.00-m-long metal bar at room temperature. A microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. The pulses are separated in time by 9.00 ms. What is the speed of sound in this metal?

Video transcript

Welcome back, everyone. We are making observations about different speeds of sound. We know that sound travels at different speeds through solids, liquids and gasses. And here's the scenario that we're given, we're told that a tap at one end of a crate that is 7.2 m long produces sound waves. Now, the sound waves are going to travel through the solid crate itself and the air, we know that the velocity of sound through air is 343 m per second. We are also told that the difference in time in which the two waves, it's the other end of the crate, the difference of 0.012 seconds between when the waves hit. And we are tasked with finding what is the velocity of the waves through the solid crate. But where can we start with this? Well, we can define our, our interval of time between when the first wave hits and the second wave hits as the following the time it takes for the waves to travel through the air minus the time it takes for the waves to travel through the solid reason, we're able to do it in that order is because waves travel faster through solids than they do air. So we know that this is equal to 0.012 seconds. Now, to find any given time time is just going to be a distance divided by a velocity. So what we can do is we can use this formula to find the time through air in conjunction with the interval we're given in order to find our solid time, which will help us find our solid velocity. So let's go ahead and do that. We have that the time it takes for the waves to travel through air, going to be the distance covered 7.2 m divided by the velocity of waves through air, which is 343. This gives us 0.02099 seconds. So now rearranging this above equation, we can say that the time it takes for the waves to travel to the solid is equal to the time it takes for the waves to travel through the air, which is 0.02099 minus our time interval of 0.012. What this gives us is that our time it takes for the waves to travel through the air is 0.00899 seconds. Wonderful. Now, multiplying our original equation for time on both sides by V and dividing both sides by t what we get is that velocity is equal to our delta X divided by time. So let's go ahead and do that and that our velocity of the waves through the solid is equal to distance covered divided by the time it takes for the waves to travel through the solid, 0.00899 which gives us a final answer of 8 0 1 m per second corresponding to our answer. Choice of B Thank you all so much for watching. I hope this video helps. We will see you all in the next one.