ckHref":"/a-level/physics/ocr/a/questions","basePath":"/a-level/physics/ocr/a/oscillations/questions","formulaUrl":null,"initialIndex":57,"initialQuestionWindow":[{"id":"e70f45a2-395a-44aa-830f-ac2849358e7f","revisionId":"4ab194b1-8b1d-447b-b493-5f2aceed4363","questionNumber":null,"questionType":"LA","specification":"A medical ultrasound transducer probe emits a longitudinal wave which travels through human muscle tissue. The speed of sound in muscle tissue is \$1540\\text{ m s}^{-1}\$. The wavelength of the emitted wave is \$0.44\\text{ mm}\$.","difficulty":4,"difficultyBand":"medium","totalMarks":5,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"a84acc3b-1078-42d2-84e1-07fa4518d67d","label":"a","content":"Calculate the frequency \$f\$ of the ultrasound wave.","markscheme":"- Recalls and rearranges wave equation to $f = \\frac{v}{\\lambda}$ M1\n- Substitutes values to find $f = \\frac{1540}{0.44 \\times 10^{-3}} = 3.5 \\times 10^6 \\text{ Hz}$ A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"wave_equation","label":"Use the wave equation","steps":[{"type":"text","order":0,"title":"Convert the wavelength","content":"The speed is in metres per second, so convert the wavelength from millimetres to metres before substituting:\n\n$$0.44\\text{ mm}=0.44\\times10^{-3}\\text{ m}=4.4\\times10^{-4}\\text{ m}.$$","highlights":[{"text":"The wavelength of the emitted wave is \$0.44\\text{ mm}\$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$v=f\\htmlData{anchor=wave_lambda}{\\color{@sky}{\\lambda}}$"},{"latex":"$$f=\\dfrac{v}{\\htmlData{anchor=divisor_lambda}{\\color{@sky}{\\lambda}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"wave_lambda"},{"color":"sky","style":"text-color","anchor":"divisor_lambda"}],"connections":[{"to":"divisor_lambda","from":"wave_lambda","color":"sky","label":"divide by wavelength"}]},"order":1,"title":"Rearrange the equation","description":"Use the wave equation, where wave speed equals frequency multiplied by wavelength. Dividing by wavelength earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=quotient}{\\color{@teal}{f=\\dfrac{1540}{0.44\\times10^{-3}}}}$"},{"latex":"$$\\htmlData{anchor=result}{\\color{@green}{f=3.5\\times10^{6}\\ \\mathrm{Hz}}}$"}],"highlights":[{"color":"teal","style":"text-color","anchor":"quotient"},{"color":"green","style":"text-color-with-background","anchor":"result"}],"connections":[{"to":"result","from":"quotient","color":"green","label":"evaluate"}]},"order":2,"title":"Substitute the values","description":"Use the wavelength already converted to metres. Correct substitution and evaluation earn A1."}]}],"generatedAt":"2026-07-20T15:29:22.557Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"b649444d-5764-42fa-8de7-eba5d79e68a6","label":"b","content":"The ultrasound wave is generated by a piezoelectric ceramic element within the transducer. The vibrating face of this element oscillates with simple harmonic motion. Calculate the maximum acceleration \$a_{\\text{max}}\$ of the vibrating face when the amplitude of its oscillation is \$1.2 \\times 10^{-8}\\text{ m}\$.","markscheme":"- Calculates angular frequency $\\omega = 2\\pi f = 2.20 \\times 10^7 \\text{ rad s}^{-1}$ (or $\\omega^2 = 4.84 \\times 10^{14} \\text{ s}^{-2}$) M1\n- Uses $a_{\\text{max}} = \\omega^2 A$ M1\n- Substitutes values to find $a_{\\text{max}} = 5.8 \\times 10^6 \\text{ m s}^{-2}$ (accept $5.80 \\times 10^6 \\text{ m s}^{-2}$ to $5.81 \\times 10^6 \\text{ m s}^{-2}$) A1","marks":3,"order":1,"markingRubric":null,"explanation":{"methods":[{"id":"frequency_then_shm","label":"Wave frequency then SHM","steps":[{"type":"text","order":0,"title":"Convert the wavelength","content":"The wave frequency is needed before using the simple harmonic motion equation. First convert the wavelength into metres:\n\n$$0.44\\text{ mm}=0.44\\times10^{-3}\\text{ m}=4.4\\times10^{-4}

Oscillations

Question 42

Oscillations Questions

Oscillations

Question 42

Oscillations Questions