Apply wave speed equation
Scenario
Bijli ki chamak pehle dikhti hai aur badal garajne ki aawaz baad mein aati hai kyunki sound ki speed light se kam hoti hai.
Hum kisi sound wave ki speed kaise calculate kar sakte hain?
Mental model
`Speed = Kadam ki lambai × 1 second mein kitne kadam`. (`Speed = Wavelength × Frequency`).
Agar aapko pata hai ki sound wave ka ek cycle kitna lamba hai (Wavelength) aur `1 second` mein kitne cycles bante hain (Frequency), toh dono ko multiply karne se total speed nikal aati hai.
Explanation
Wave speed ka equation ek fundamental formula hai jo sound, light, aur kisi bhi dusri wave par apply hota hai. Iska basic idea bahut simple hai: speed ka formula `v = d / t` hota hai.
Ek complete wave cycle ke liye, distance covered `d` hoti hai **Wavelength** (`λ`) aur usko poora karne ka time `t` hota hai **Time Period** (`T`). Toh hum likh sakte hain ki speed `v = λ / T`.
Kyunki hum jaante hain ki frequency `ν = 1 / T`, isliye hum `1 / T` ki jagah `ν` likh sakte hain. Isse hamara main wave speed equation banta hai: `v = λ × ν`.
Is equation (`Speed = Wavelength × Frequency`) ka matlab hai ki agar kisi given medium mein sound ki speed constant hai (jaise air mein approx `340 m/s`), toh wavelength aur frequency ek doosre ke inversely proportional hote hain. High frequency wali sound ki wavelength choti hogi, aur low frequency ki wavelength badi hogi.
Worked example
Problem: A sound wave has a frequency of `2 kHz` and wavelength `35 cm`. Find the speed of the wave.
- Sabse pehle values ko unki SI units mein convert karenge. Frequency `Hz` mein aur wavelength meters mein.
- Ab wave speed equation lagayenge.
- Values put karke speed calculate karenge.
Answer: `700 m/s`
Problem: A submarine sends a sonar signal with a frequency of `50 kHz`. If the speed of sound in seawater is `1500 m/s`, what is the wavelength of the sonar wave?
- Is baar speed aur frequency di hui hai, toh formula ko rearrange karenge wavelength ke liye.
- Frequency ko `Hz` mein convert karke values daal kar solve karenge (`50 kHz = 50000 Hz`).
Answer: `0.03 m` (or `3 cm`)
Key points
- Wave Speed Equation: `v = λ × ν` (`Speed = Wavelength × Frequency`)
- Constant Speed in a Medium: For a given medium under same conditions, the speed of sound remains nearly constant.
Common mistakes
- Forgetting unit conversions: Students formula lagane se pehle `kHz` ko `Hz` mein aur `cm` ko meters mein convert karna bhool jate hain.
Recall questions
- What is the relationship between speed, wavelength, and frequency?
- If frequency is doubled and speed remains constant, what happens to the wavelength?
- What happens to the speed of sound if we change the frequency in the same medium?
Questions & answers
A sound wave has a frequency of 2 kHz and wave length 35 cm. How long will it take to travel 1.5 km?
First find speed: v = 0.35 * 2000 = 700 m/s. Time = Distance / Speed = 1500 / 700 = 2.14 s.
Approach: Use the wave speed equation to find velocity, then apply basic kinematic formula t = d/v.
Write the formula relating speed, wavelength, and frequency.
Speed (v) = Wavelength (λ) × Frequency (ν)
Approach: State the wave equation clearly.
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