- #1
snowcrystal42
Hi,
I'm trying to solve two problems related to standing waves and wave interference; while I'm not having difficulty with the actual solving portion, I don't know if I'm interpreting the questions correctly. Question 1: "A violin string is tuned to 460 Hz (fundamental frequency). When playing the instrument, the violinist puts a finger down on the string 1/3 of the string length from the neck end. What is the frequency of the string when played like this?"
Relevant equations:
v = √(T/μ) where μ is the linear mass density of the string
For a string fixed at both ends L = ½(nλ) or ƒn=(nv)/(2L)
I don't really know much about instruments, but am I correct in thinking that if the string is fingered 1/3 from the neck end, then the vibrating portion will be 2/3 the original length? Which means that the new frequency will be 3/2 as large?
I also have a quick question on wave interference:
Question 2: (A figure is given showing two speakers and a listener located somewhere between them.) "The speakers vibrate out of phase...what is the fourth closest distance to speaker A that speaker B can be located so that the listener hears no sound?"
Relevant equations: For speakers out of phase, destructive interference: ΔL = nλ where n = 0,1,2,3...
Just to check, the "fourth closest distance" includes when n = 0 (when the path differences between the listener and both speakers are the same), right? So I would use n = 3?
Thanks!
I'm trying to solve two problems related to standing waves and wave interference; while I'm not having difficulty with the actual solving portion, I don't know if I'm interpreting the questions correctly. Question 1: "A violin string is tuned to 460 Hz (fundamental frequency). When playing the instrument, the violinist puts a finger down on the string 1/3 of the string length from the neck end. What is the frequency of the string when played like this?"
Relevant equations:
v = √(T/μ) where μ is the linear mass density of the string
For a string fixed at both ends L = ½(nλ) or ƒn=(nv)/(2L)
I don't really know much about instruments, but am I correct in thinking that if the string is fingered 1/3 from the neck end, then the vibrating portion will be 2/3 the original length? Which means that the new frequency will be 3/2 as large?
I also have a quick question on wave interference:
Question 2: (A figure is given showing two speakers and a listener located somewhere between them.) "The speakers vibrate out of phase...what is the fourth closest distance to speaker A that speaker B can be located so that the listener hears no sound?"
Relevant equations: For speakers out of phase, destructive interference: ΔL = nλ where n = 0,1,2,3...
Just to check, the "fourth closest distance" includes when n = 0 (when the path differences between the listener and both speakers are the same), right? So I would use n = 3?
Thanks!