Two guitarists attempt to play the same note of wavelength 64.8 cm at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength 65.2 cm instead. What is the frequency of the beats these musicians hear when they play together?

Video transcript

Hey everyone in this problem. Two violinists are tuning their equipment to simultaneously play a note of wavelength 773 mm. However, one piece of equipment produces a note of wavelength 767 mm, which is different from that desired wavelength were asked to determine the beat frequency an observer will detect from the two pieces of equipment played together. Alright, so let's recall that the beat frequency F beat. Ok, is equal to the magnitude of the difference of the two frequencies. Okay, this is gonna be the magnitude of F one minus F two. Okay, let's take the absolute value. Alright, so what were we given in the problem? We're given wavelengths. Okay, so we're gonna call the wavelength λ one. Okay. That desired wavelength of 773 mm. And we'll call λ to the other wavelength produced 767 mm. Now we want to go ahead and convert these into our standard unit of m. Okay, so this is going to be equal to 773 mm times one m per 1000. Okay, the unit of millimeters will cancel. We divide by 1000 we get 0. m. Okay, and we can do the same for lambda 2, 776 millimeters times one m per 1000 mm. Okay, so we divide by 1000 we get 0.767 m. All right, so our FB. Okay, this Equation for the beat frequency requires us to find F one and F two. The frequencies of those two Um Sounds okay? We don't have the frequencies but we do have the wavelength. Okay, so let's recall the relationship between frequency and wavelength and we have that the speed V. Is equal to the frequency F times the wavelength lambda. Okay. And if we arrange we rearrange this. Okay, this is gonna tell us that the frequency F one is going to be equal to V over lambda one. And similarly the frequency F two is going to be equal to V over the wavelength lambda two. So our frequency is the speed divided by the wavelength. Now we're talking about the speed of sound here. So we're gonna use 343 m/s. That approximate value. We're gonna divide by our wavelength of 0.773 m. And we get a frequency F one, approximately 443. hertz. Okay, similarly, for F. Two, we have the speed of sound. 343 m per second divided by lambda. To that wavelength. 0.767 m. Okay. The unit of meters cancel. And we're left with the unit of hertz When we get 447 .2 Hz here. Alright, now we know our frequencies F one and F. two. We want to find the beat frequency. Okay. And again it's going to be the magnitude of the difference. So we have the beat frequency F Beat is equal to the absolute value of F one minus F. Two is equal to the absolute value of 443.73 hertz minus 447.2 hertz. And which gives us a beat frequency of 3.47 Hz. Alright, so that is our beat frequency for these two violins that are playing slightly different wavelengths. So if we look at our answer traces, we see that we have answered d. Hz for our beat frequency. Thanks everyone for watching. I hope this video helped see you in the next one.