- #1

K_Physics

- 9

- 0

## Homework Statement

String

*A*is stretched between two clamps separated by distance

*L*. String

*B*, with the same linear density and under the same tension as string

*A. String B*is stretched between two clamps separated by distance 4

*L*. Consider the first eight harmonics of string

*B*. For which of these eight harmonics of

*B*(if any) does the frequency match the frequency of (a)

*A*’s first harmonic, (b)

*A*’s second harmonic, and (c)

*A*’s third harmonic?

Not sure if I correctly solved the problem (hopefully I did =D). Just need someone to check over my work =D. Thanks!

## Homework Equations

ν = √(T/μ)

ν = ƒλ

**[/B]**

L = n

L = n

**λ/2**

ν: Velocity

T: Tension

μ: Linear Density

ƒ: Frequency

λ: Wavelength

L: Length

n: nth Harmonicν: Velocity

T: Tension

μ: Linear Density

ƒ: Frequency

λ: Wavelength

L: Length

n: nth Harmonic

## The Attempt at a Solution

[/B]

Since the tension and linear density on both strings are equal, the velocity is also equal.

**Next I solved for the frequency of system B:**

ν = ƒλ

ƒ = ν/λ → 1

L = nλ/2, since L = 4L

λ = 8L/n → 2

Subbing 2 → 1

ƒ = νn/8L

--------------------------------------------------------------------------------

First Harmonic of String A:

ƒ = νn/8L

--------------------------------------------------------------------------------

First Harmonic of String A:

L= λ/2 ⇒ λ = 2L

ƒ=ν/λ ⇒ ƒa1 = ν/2L

ƒa1 = ƒb

ν/2L = νn/8L

**n = 4 (between 1-8)**

**Second Harmonic of String A:**

L= λ

ƒ=ν/λ ⇒ ƒa2 = ν/L

ƒa2 = ƒb

ν/L = νn/8L

**n = 8 (between 1-8)**

**Third Harmonic of String A:**

L= 3λ/2 ⇒ λ = 2L/3

ƒ=ν/λ ⇒ ƒa3 = 3ν/2L

ƒa3 = ƒb

3ν/2L = νn/8L

**n = 12 (not between 1-8)**