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#frequency change

2 public questions tagged with this topic.

Equations of SHM, Phase and Angular Frequency

What happens to the frequency of a spring-mass system if the spring constant is quadrupled and the mass is halved?

**SHM representation** using sine or cosine equivalent with phase offset, ω relates to system parameters like mass and stiffness. Understanding ω and φ permits prediction of position at any time and comparison of two SHM via phase difference Δφ = φ₂ - φ₁. Frequency v = (1/2π) √((k/m)) . If k' = 4k and m' = (m/2) , then v' = (1/2π) √((4k/m/2)) = (1/2π) √((8k/m)) = √(8) · v = 2√(2) · v , doubling the original frequency by √(2) . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result

Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency

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Stationary Waves and Standing Waves in Strings

What is the effect on a standing wave’s frequency if the length of the vibrating medium is halved?

**Standing wave in fixed string** has nodes at ends, quantizing modes. Fundamental n=1 has λ₁ = 2L, higher harmonics multiples of fundamental f₁. Third harmonic n=3 has three half-wavelengths in length L, f₃ = 3v/(2L), illustrating standing wave condition and boundary enforcement. For a standing wave, v_n = (n v/2L) . Halving the length L to L/2 gives v_n' = (n v/2 · (L/2)) = (n v/L) = 2 · (n v/2L) , doubling the frequency. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Doubles, illustrating frequency-length-speed interdependence and quantiza

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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